The sparse Blume-Emery-Griffiths model of associative memories

We analyze the Blume-Emery-Griffiths (BEG) associative memory with sparse patterns and at zero temperature. We give bounds on its storage capacity provided that we want the stored patterns to be fixed points of the retrieval dynamics. We compare our results to that of other models of sparse neural networks and show that the BEG model has a superior performance compared to them.Comment: 23 p

Gradation of Algebras of Curves by the Winding Number

We construct a new grading on the Goldman Lie algebra of a closed oriented surface by the winding number. This grading induces a grading on the HOMFLY-PT skein algebra and related algebras. Our work supports the conjectures of B. Cooper and P. SamuelsonComment: Changed acknowledgments and Definition 2.

Inelastic neutron scattering study of binding of para-hydrogen in an ultra-microporous metal-organic framework

Metal-organic framework (MOF) materials show promise for H2 storage and it is widely predicted by computational modelling that MOFs incorporating ultra-micropores are optimal for H2 binding due to enhanced overlapping potentials. We report the investigation using inelastic neutron scattering of the interaction of H2 in an ultra-microporous MOF material showing low H2 uptake capacity. The study has revealed that adsorbed H2 at 5 K has a liquid recoil motion along the channel with very little interaction with the MOF host, consistent with the observed low uptake. The low H2 uptake is not due to incomplete activation or decomposition as the desolvated MOF shows CO2 uptake with a measured pore volume close to that of the single crystal pore volume. This study represents a unique example of surprisingly low H2 uptake within a MOF material, and complements the wide range of studies on systems showing higher uptake capacities and binding interactions

Design of stable mixed-metal MIL-101(Cr/Fe) materials with enhanced catalytic activity for the Prins reaction

This work highlights the benefit of designing mixed-metal (Cr/Fe) MOFs for enhanced chemical stability and catalytic activity. A robust and stable mixed-metal MIL-101(Cr/Fe) was prepared through a HF-free direct hydrothermal route with Fe3+ content up to 21 wt%. The incorporation of Fe3+ cations in the crystal structure was confirmed by 57Fe Mössbauer spectrometry. The catalytic performance of the mixed metal MIL-101(Cr/Fe) was evaluated in the Prins reaction. MIL-101(Cr/Fe) exhibited a higher catalytic activity compared to MIL-101(Cr), improved chemical stability compared to MIL-101(Fe) and a higher catalytic activity for bulky substrates compared to MIL-100(Fe). In situ infra-red spectroscopy study suggests that the incorporation of Fe3+ ions in MIL-101 structure leads to an increase in Lewis acid sites. It was thus concluded that the predominant role of Cr3+ ions was to maintain the crystal structure, while Fe3+ ions enhanced the catalytic activity

Post-synthetic Mannich chemistry on metal-organic frameworks: system-specific reactivity and functionality-triggered dissolution

The Mannich reaction of the zirconium MOF [Zr6O4(OH)4(bdc-NH2)6] (UiO-66-NH2, bdc-NH2 = 2-amino-1,4-benzenedicarboxylate) with paraformaldehyde and pyrazole, imidazole or 2-mercaptoimidazole led to post-synthetic modification (PSM) through C–N bond formation. The reaction with imidazole (Him) goes to completion whereas those with pyrazole (Hpyz) and 2-mercaptoimidazole (HimSH) give up to 41% and 36% conversion, respectively. The BET surface areas for the Mannich products are reduced from that of UiO-66-NH2, but the compounds show enhanced selectivity for adsorption of CO2 over N2 at 273 K. The thiol-containing MOFs adsorb mercury(II) ions from aqueous solution, removing up to 99%. The Mannich reaction with pyrazole succeeds on [Zn4O(bdc-NH2)3] (IRMOF-3), but a similar reaction on [Zn2(bdc-NH2)2(dabco)] (dabco = 1,4-diazabicyclo[2.2.2]octane) gave [Zn3(bdc-NH2)1.32(bdc-NHCH2pyz)1.68(dabco)]·2C7H8 5, whereas the reaction with imidazole gave the expected PSM product. Compound 5 forms via a dissolutionrecrystallisation process that is triggered by the 'free' pyrazolate nitrogen atom competing with dabco for coordination to the zinc(II) centre. In contrast, the 'free' nitrogen atom on the imidazolate is too far away to compete in this way. Mannich reactions on [In(OH)(bdc-NH2)] (MIL-68(In)-NH2) stop after the first step, and the product was identified as [In(OH)(bdc-NH2)0.41(bdc-NHCH2OCH3)0.30(bdc-N=CH2)0.29], with addition of the heterocycle prevented by steric interactions

Study of Xenon Mobility in the Two Forms of MIL-53(Al) Using Solid-State NMR Spectroscopy

The Al-based metal–organic framework (MOF) MIL-53­(Al) exhibits a structural transition between a large-pore (<i>lp</i>) form and a narrow-pore (<i>np</i>) one. Such change is induced by temperature, external pressure, or the adsorption of guest molecules. ¹²⁹Xe solid-state NMR experiments under static and magic-angle spinning (MAS) conditions have been used to study the <i>lp</i>–<i>np</i> transition in MIL-53­(Al) initially loaded with xenon gas under a pressure of 5 × 10⁴ Pa (at room temperature). The conversion of the <i>lp</i> form into the <i>np</i> one when the temperature decreases from 327 to 237 K and the reopening of the pores below 230 K are then observed. Furthermore, ¹H → ¹²⁹Xe cross-polarization under MAS (CPMAS) experiments demonstrate the possibility to observe the <i>np</i> phase at <i>T</i> ≤ 230 K, while the <i>lp</i> one is unseen because the xenon residence time is too short for successful cross-polarization transfer. Moreover, even for the <i>np</i> phase at 199 K, the xenon atoms still exhibit significant motion on time scale faster than a few milliseconds. We prove the exchange of Xe atoms between the <i>lp</i> and <i>np</i> forms at room temperature with the two-dimensional (2D) ¹²⁹Xe EXchange SpectroscopY (EXSY) NMR method. Using ¹²⁹Xe selective inversion recovery (SIR) experiments, the rate for this exchange has been measured at 43 ± 6 s^–1

A novel bismuth-based metal-organic framework for high volumetric methane and carbon dioxide adsorption

Solvothermal reaction of H4L (L = biphenyl-3,3’,5,5’-tetracarboxylate) and Bi(NO3)3·(H2O)5 in a mixture of DMF/MeCN/H2O in the presence of piperazine and nitric acid at 100 oC for 10 h affords the solvated metal-organic polymer [Bi2(L)1.5(H2O)2]·(DMF)3.5·(H2O)3 (NOTT-220-solv). A single crystal X-ray structure determination confirms that it crystallises in space group P2/c and has a neutral and non-interpenetrated structure comprising binuclear {Bi2} centres bridged by tetracarboxylate ligands. NOTT-220-solv shows a 3,6-connected network having a new framework topology with a {4·62}2{42·65·88}{62·8} point symbol. The desolvated material NOTT-220a shows exceptionally high adsorption uptakes for CH4 and CO2 on a volumetric basis at moderate pressures and temperatures with a CO2 uptake of 553 gL-1 (20 bar, 293 K) with a saturation uptake of 688 gL-1 (1 bar, 195 K). The corresponding CH4 uptake of 165 V(STP)/V (20 bar, 293 K) and 189 V(STP/V) (35 bar, 293 K) is within the top three MOF materials under the same conditions, surpassed only by PCN-14 and Ni-MOF-74 (230 and 190 V(STP)/V 35 Bar, 298 K). The maximum CH4 uptake for NOTT-220a was recorded at 20 bar and 195 K to be 287 V(STP)/V, while H2 uptake of NOTT-220a at 20 bar, 77 K is 42 gL-1. These gas uptakes have been modelled by Grand Canonical Monte Carlo (GCMC) and Density Functional Theory (DFT) calculations, which confirm the experimental data and give insights into the nature of the binding sites of CH4 and CO2 in this porous hybrid material